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[Phys-l] The Ontology of Mass



The Ontology of Mass


In the delightful book "The Lightness of Being, Mass, Ether and the
Unification of forces" by Frank Wilczek DR Wilczek makes clear the central
nature of the property of nature we call mass. Mass all too often is thought of
as merely "frozen energy" but thinking this way may miss some interesting
aspects of mass. Of particular interest to me is the relationship between
mass and time. In this post I'll try to make this connection.

As far as we know the property of mass has two origins. These are

1) Scalar fields related to symmetry breaking


2) Confinement mass, that is mass related to systems of quanta
confined in a region of space by color field interactions.


In the 5% of the Universe that makes up what we can directly observe
with our eyes and instruments all but a few percent of mass is the result of
mechanism 2 above. Only a few percent of all the mass is believed to be the
result of coupling to a weak charged scalar field responsible for
electroweak symmetry breaking, known as the Higgs field. It is hoped that we may
soon see the quanta of this field at the LHC at CERN.

However, in the 25% of the Universe we call Dark Matter, it may well be
that all of the mass is the result of coupling to some different scalar field
based on higher energy symmetry breaking events. I will offer some
speculation on this, but in reality we simply don't know what dark matter really
is, and we may be in for some surprises.

The best model we have for describing the particle physics symmetry at very
high energy is the SO(10) Gut model. This model leads to a series of
symmetry breaking events.

We can deform SO(10) as


SO(10) = SU(4)_ps X SU(2)_L X SU(2)_R


Where gives us the left and right handed fields in unity with the
Pati Salem field. This leads to the first symmetry breaking event


SU(4)_ps X SU(2)_L X SU(2)_R = SU(3)_c X SU(2)_L XU(1)_B-L


Here we get a new vector field which couples to B-L charge. This
new field looks very much like a Gravivector field so we may speculate
that the scalar field associated with this symmetry breaking event is the
Gravisccalar field known also as the Dilaton field. This scalar field would
couple to the B-L quanta causing its quanta to become a massive boson. This
would suppress coupling to the B-L charge, limiting this force at lower
energy to a very short range.

At still lower energy we would get

SU(3)_c X SU(2)_L XU(1)_B-L = SU(3)_c X SU(2)_LX U(1)_Y


Giving us the Hypercharge field. Possibly the scalar field related to
this event is a Higgs like field coupled to the right handed weak field.
This scalar field would couple to the quanta of this field to suppress right
handed weak charge to very short range also making this interaction
unobservable at the current energies available to us.


This would gives two new fields, the Hypercharge and Z prime fields as
mixtures of the third component of the right handed field.


{ A_Y, Z_Y } = Exp[ i*phi_z*sigma_y]* { A_ (B_L) , W^3_R}


Where phi_z the mixing angle equal to 33.21 degrees based on a
nonchiral electromagnetic field and the measured mixing angles in electroweak
theory.


And finally the event


SU(3)_c X SU(2)_LX U(1)_Y= SU(3)_3 X U(1) + SU(3) X SU(2)_w


Gives us the standard model symmetry and;


{ A_em, Z_w } = Exp[i*phi_w*sigma_y] * { A_Y, W^3_L}


Where phi_z the weak mixing angle equals 28.7 degrees and the scalar field
being the Higgs field.


The Higgs field is responsible for a few percent of mass in the
standard model the rest being due to mechanism 2as related above.


While the Mathematical treatment of confinement mass involves very
difficult computer calculations based on the Lattice model we can devise a toy
model to illustrate how this works.


Given two or more quarks and/or anti quarks confined by the color force the
total energy of the system is the sum of the localization energy and the
color field potential. Therefore


E= k_1/R + k_2*R


Where R is the distance between quarks, k_1 is the constant related to
the uncertainty principle and k_2 is the effective color force coupling value
based on complex lattice calculations. So we find R by having this system
in its lowest energy.

dE/dR= - k_1/R^2 + k_2 =0

R= sqrt[k_1/k_2]




Now having presented a basic description for the origin of mass we will see
how mass relates to time. ( Note I have ignored SUSY breaking which is
another important source of mass generation based on mechanism 1 but the
details here are even more uncertain so I won't even offer any speculation on
this, hopefully this will be sorted out at CERN in the next year or so.)


In the Universe the entropy for any given Hubble volume is given by


S= k*ln D^N

Where k is a constant, D is the degrees of freedom of all Quantum fields
and N is the number of quanta.

This gives us approximately


S=N


N= E/E_min= E*lambda/(h*c)

If we confine the Quantum fields to the boundary we get

S= 2*pi*R*E/(h*c)

which is the Bekenstein bound.

Putting all constants to unity we have

S=R*E


Given a Universe of massless quanta we have


S=R*rho*R^3 = R(1/R^4)*R^3=1

So we find in a Universe absent massive quanta

dS/dR =0

Such a Universe has no arrow of time.

In a Universe with massive particles we get


S= R*(1R^3)*R^3 = R


S=R

The arrow of time relates to size of the Hubble volume.

Mass also relates to time in special relativity. Generally it is asserted
that the relativistic equation have two basis solutions, which we relate to
matter and anti matter. In these solution mass is always a positive value.
But in reality the relativistic equations have four solutions which include
negative mass solutions. These "extra" solutions were demonstrated to be
unphysical by Pauli. Some physicists have attempted to resurrect these
solutions to solve the cosmological constant problem but I won't go into any
detail on these ideas here. Very simply we can look at the equations of SR.


c= t(0)=1


gamma= 1/sqrt[ 1-v^2/c^2]



E= gamma*m

P=gamma*m*v_g

t=1/gamma

t= m/E

v_g=P/E v_phase= E/P

s=v*t

We have


MATTER



E(+)= gamma(+)*m(+)

P(+)=gamma(+)*m(+)*v_g (+)

t(+)=1/gamma (+)

t(+)= m(+)/E(+)

v_g(+)=P(+)/E(+) v_phase(+)= E(+)/P(+)

s(+)=v(+)*t(+)



Psi= psi(0*Exp[ -i*(w*t-k*x)]


ANTI MATTER



E(-)= gamma(-)*m(+)


P(-)=gamma(-)*m(+)*v_g (+)


t(-)=1/gamma (-)

t(-)= m(+)/E(-)

v_g(+)=P(-)/E(-) v_phase(+)= E(-)/P(-)

s(-)=v(+)*t(-)

Psi= psi(0*Exp[ i*(w*t-k*x)]


And the unphysical solutions

NEGATIVE MATTER


E(-)= gamma(+)*m(-)


P(+)=gamma(+)*m(-)*v_g (-)


t(+)=1/gamma (+)

t(+)= m(-)/E(-)

v_g(-)=P(+)/E(-) v_phase(-)= E(-)/P(+)

s(-)=v(-)*t(+)

Psi= psi(0*Exp[ -i*(w*t+k*x)]


NEGATIVE ANTI MATTER


E(+)= gamma(+)*m(-)


P(-)=gamma(-)*m(-)*v_g (-)


t(-)=1/gamma (-)

t(-)= m(-)/E(+)

v_g(-)=P(-)/E(+) v_phase(-)= E(+)/P(-)

s(+)=v(-)*t(-)

Psi= psi(0*Exp[ i*(w*t+k*x)]



The point here is that given m=0 for any solution time flow is
zero in the local frame. In a Universe where every quanta has a zero mass, the
concept of time has no meaning. Interestingly the full set of particle
solutions show up in String theory cosmology. In the model proposed by
Venziano and Gasperini by equating T duality and time reversal all four sets of
solutions are present in the Wheeler De Witt equation.

Given

{ pd_phi^2-pd_b^2+lambda_str*V(b,phi)*Exp[-2*phi]}*Psi(b,phi)=0



Where

b=sqrt[D]*lna

D is the number of dimension in super space


phi= theta-sqrtD]*b- ln[ intd^D X/ lambda_str


b is the spacelike parameter and phi is the timelike parameter/

Psi_m = exp[-ik*(b-phi)]

Psi_am = exp[ik*(b-phi)]

Psi_nm= exp[-ik*(b+phi)]

Psi_nam= exp[ik*(b+phi)]


This gives four cosmological solutions the two physical solutions


Matter- A Universe expanding post Big Bang

Anti Matter- A Universe contracting pre Big Bang


And the unphysical solutions based on T Duality


Negative Matter- A Universe contracting post Big Bang


Negative Anti Matter- A Universe expanding Pre Big Bang.

We can factorize the partition function of these solutions based on a model
proposed by Kaplan and Sundrum


Z= { Int D(Psi_m) exp[i* Int sqrt[-g]*L_m} *{ Int D(Psi_nm) exp[-i*Int
sqrt[-g]*L_nm}


With both path integrals related by T duality. The link illustrates this
with a useful diagram.


Bob Zannelli







_http://www.ba.infn.it/~gasperin/_ (http://www.ba.infn.it/~gasperin/)